I think your conclusion is correct. Majority of the lenses designed for 135 (so-called "FF") format are not capable to resolve 20 Mp FF sensors (20 Mp m43 has the same pixel pitch as 80Mp FF).
"
20 Mp FF.." is misstyping. Instead it should be typed "80 Mp FF.."
That sounds like nonsense, unless by "lenses designed for 135" you actually mean all lenses designed since that format's inception. Or you have a pretty loose definition of what "most" means.
One should have in mind that majority of FF lenses have insufficient resolution for pixel density of m43 sensors.
That makes more sense and is much easier to argue for, but are you sure about this?
Me and some my collegues (physisists), we were testing a lot of FF-lenses during our life using not just images from a camera, but with a special optical bench. The best FF-lenses showed about 100 lp/mm (line pairs per millimiter) at an image center and f/5.6 according to the Rayleigh criterion. It is a very good resolution for 16 Mp FF-sensor, but it is not enough for m43 16Mp sensor.
Now, let me show that, for example, Panasonic 20 f/1.7 can provide a resolution higher than 200 lp/mm.This fact can be well demonstrated by the first photo and by its cropped version (photo 2) below.

Photo 1
Thus our object shown in Photo1 has a total width of 100 mm.
Now let us look at a central part of this image.

Photo 2
As you can see, in the central part we have images of different gratings which are marked as "5", "7"..."20".
The mark "5" means 10 line pairs per one cm of the ruller. The mark "20" means 40 printed lines per one centimeter. The gratings "12", "15", "17" and "20" are not resolved by the sensor, but it doesn't mean that they are not resolved by the lens.
The m43 sensor has a width of 17.3 mm.
It means that if the grating "20" is resolved
by the lens then the lens is characterized by a resolution of 40 lp/mm*100mm/17.3mm = 230 lp/mm.
As I have said the grating "20" is not resolved
by 16Mp sensor in this case (the image of this grating is shown in photo 3 made with a longer lens from the same distance). But, why I can claim that Panasonic 20 f/1.7 lens does resolve the grating "20" ? It is because in photo 2 one can see a pronounced aliasing effect from the gratings "12" up to the grating "20".
The existance of the well visible aliasing effect on the "20"-grating prooves that the signal from the lens does contain a spectral component with a spatial frequency of 230 1/mm, or the lens, at least according to the Rayleigh criterion, resolves not less than 230 lp/mm. The last statement, of course, can be proved mathematically, but this forum is not a good place for that, so at this moment you have just to beleave me. The 20 f/1.7 can resolve an m43 sensor with more than 40 Mp (the FF lense should resolve more than 160Mp FF sensor to be in the same resolution league)!

photo 3
The guys at lenstip did measure the resolution that the Canon 5Ds R is capable of delivering. They got 80 lpmm out of it (with existing FF glass, obviously). For reference, E-M5 II is capable of 88 lpmm, and PEN-F a whooping 95 lpmm.
All the tests including ones from guys at lenstip are restricted by sensor resolution and AA-filters plased before sensors. Thus these tests, unfortunately, can not tell us on a real lens resolution.
In my case I have used the fact that if AA-filter is absent then the true lens resolution can be estimated from the aliasing effect.
The 20 f/1.7 is, of course, one of the best lenses. But I have also tested many of the other lenses (14 mm f/2.5, Panasonic 12-35 f/2.8, panasonic 14-42 PZ, panasonic 14-140ii, olympus 14-42 EZ et.al).
All the lenses I tested have sweet settings, when they do outresolve the 16 Mp sensor at least in a central part of an image. And everybody who has HR mode can check this at f/5.6 and lower f-numbers (f/8 is just at difraction edge, so improvement at f/8 will not be well visible in HR mode). My advise - be critical to test results (I mean absolute values in lp/mm or Mpix) provided by such "experts" as DXO, which do not have a relation to the lenses itself !
Unfortunately, at least the budgett FF lenses are indeed very bad in a sense of their true optical resolution. I am not sure that in future it will be possible to make good lenses for say FF 80 Mp sensor (even using an expansive glass) without a significant increase of a lens diameter compared to the existing FF lenses. So it is quite possible that in future good FF lenses will be even more heavy than we have for the moment.
Interestingly, 12mp MFT cameras reach about 80 lpmm, which is the same as with 5Ds R. Which is not surprising considering the pixel density is very similar.
Obviously, this is for the best lenses. The kit zooms for MFT are nowhere near to resolving 80 lpmm. So you could actually argue that: majority of MFT lenses have insufficient resolution for pixel density of m43 sensors.